Contemporary image processing methods apply image data transforms in a vast array of applications. In many cases, the transformation process causes a loss of data and frequently requires complex image data compression and decompression circuitry for image transmission and restoration. Lossless image transformation processes are generally perceived as being computationally expensive and tend not to be used as often as lossy transformation processes. Among the most widely used image data transforms are the wavelet transform and the color transform.
The processing of image data also requires sophisticated methods for manipulating data stored in multi-dimensional matrices. At times, such data can be highly position dependent and any processing on such data may require certain types of highly localized processing given the unique nature of the interactions between image data at neighboring locations. These matrices may also be comprised of different types of numerical values. Frequently, such matrices include real number entries that are applied to an input data set that may also be comprised of real numbers or other types of numerical data. In the event integer input data is provided, the output image data produced by a transformation matrix comprised of real numbers may not necessarily provide the most accurate mapping of input data values to output data values. Furthermore, the reliable mapping of entire classes of numerical data may require the processing of bounded and unbounded length input data vectors.
A reliable image data transformation process is needed that can be used to map integer input data to integer output data without the possible loss of data associated with the transformation of such input data by transformation matrices including real number entries. This process must be capable of being applied to the most widely used transforms for input data vectors that are bounded and unbounded in length. The present invention is directed to providing computer-implemented methods for generating integer-to-integer transformation matrices that are approximations to known linear transformation matrices.